How do I change the default data settings for an empty?
There's no mechanism to change the default, or setting in preferences. It could be added but frankly it's not likely to be considered worth the effort.



When creating the Empty it is picked from a dropdown menu, the next menu item down is Arrows. Moving a few pixels down with the mouse is probably the most non-invasive solution.  

Existing key-combos  

But by far the easiest is the shortcut sequence Shift + A  >  E  >  A  

Making an add-on  

But you could write an add-on / operator and bind it to a shortcut to make Arrows the default display type for Empties generated by the operator. See this post for most of the code you'd need.

Add Shortcut 

You can also make a shortcut, by right-clicking on the Arrows menu item and choosing Add Shortcut, and it will ask you to press a key or combo.